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Extra info for 1996 IEEE International Conference on Systems, Man and Cybernetics
We have to construct a strictly increasing chain of stable relations satisfying the conditions WM1– WM3. In  it is shown that every non-trivial aperiodic automaton admits a non-trivial stable partial order. Let ρ1 be such an order with respect to A and π1 = Eq(ρ1 ). The quotient automaton A /π1 is aperiodic again because its transition monoid is a quotient of the transition monoid of A . Thus, A /π1 preserves a chain of partial orders by the induction assumption. Lifting this chain back to Q, we obtain, for some , a chain of stable relations ρ0 ⊂ ρ1 ⊂ · · · ⊂ ρ satisfying WM2 and WM3 and such that ρ0 = π1 .
LNCS, vol. 3472, pp. 5–33. Springer, Heidelberg (2005) ˇ 14. : The Cern´ y conjecture for aperiodic automata. Discrete Math. Theoret. Comp. Sci. fr 1 2 Abstract. Finite languages and ﬁnite subsequential functions can be represented by possibly cyclic ﬁnite machines, respectively called cover automata and cover transducers. In general, reduced cover machines have much fewer states than the corresponding minimal machines, yielding a compact representation for lexicons or dictionaries. We present here a new algorithm for reducing the number of states of an acyclic transducer.
This paper addresses the acyclic case, where the input is a transducer that realizes the function. ): CIAA 2007, LNCS 4783, pp. 38–50, 2007. Jan Holub and Jan Zd’´ c Springer-Verlag Berlin Heidelberg 2007 Reducing Acyclic Cover Transducers 39 of a state, for 0 ≤ k ≤ l, that is the restriction to Σ ≤k of the right function. The notion of preﬁx k-function is introduced, and a new algorithm is described, based on the computation of preﬁx k-functions. Moreover, a new technique involving linearly dependent preﬁx k-functions is discussed.